A Pareto Front Transformation Model for Multi-objective-based Constrained Optimization

Abstract

One of the most promising approaches of handling constrained optimization problems (COPs) is to adopt multi-objective methods, which can provide a trade-off between the objective and constraints. However, the multi-objective-based constraint-handling techniques take preference over infeasible solutions, some promising feasible solutions cannot survive during the course of search because they are dominated ones. Furthermore, some nondominated infeasible solutions with worse objective values should not be reserved in that they are far from the feasible optimal solution. To address these two problems, this paper proposes a Pareto front transformation model which transforms a part of potential feasible solutions into nondominated ones. Meanwhile, combined with the dynamic multi-objective technique, certain nondominated infeasible solutions with worse objective values will be rejected. In this way, the search can towards the global optimum from both the feasible and infeasible sides of the search space. The proposed Pareto front transformation model is integrated into a multi-objective-based constrained evolutionary algorithm (CEA). The new designed algorithm is named PT-MOEA, and it is compared with seven peer multi-objective-based CEAs and five state-of-the-art CEAs on solving IEEE CEC 2006 and IEEE CEC 2010 test suites, respectively. Experimental results demonstrate the competitiveness of the proposed method in comparison with its competitors for solving COPs.

Constrained Optimization Based on Ensemble Differential Evolution and Two-Level-Based Epsilon Method

“…The multiobjective-based methods usually introduce some additional objective function to form a new problem and then employ the concept in the multiobjective optimization community to solve it [23]- [25]. However, the application of these methods still faces some challenges because solving multiobjective optimization problems is still quite challenging in and of itself.…”

“…Zeng et al proposed Pareto front transformation model to retain some promising dominated feasible vectors and nondominated infeasible ones with worse objective. Thus the search within both the feasible and infeasible region is allowed [25].…”